作者：石兆羽1,2, 杨绍普1,2, 赵志宏2
作者单位：1. 石家庄铁道大学机械工程学院, 河北 石家庄 050043;
2. 河北省交通安全与控制重点实验室, 河北 石家庄 050043
关键词：耦合系统;Van der Pol-Duffing振子;混沌;微弱信号检测
摘要：
传统方法检测微弱信号具有一定的困难，利用混沌振子对微弱信号敏感以及对强噪声具有良好免疫力的特性，提出基于耦合Van der Pol-Duffing振子系统检测微弱信号的新方法。对比不同参数下耦合系统的动力学行为，通过分岔图和二分法确定临界阈值，保证阈值搜索速度和阈值精度。阐述基于相图的微弱信号检测原理，通过从混沌态到周期态的转变成功检测淹没在强噪声中的微弱信号，信噪比门限达到-30 dB。同时考察不同精度幅值下噪声对系统状态的影响，不同频率信号以及相移对检测的影响。仿真结果表明，该耦合系统在强噪声条件下对微弱信号敏感，用于检测微弱信号是可行的。
Research on weak signal detection based on coupled Van der Pol-Duffing system
SHI Zhaoyu1,2, YANG Shaopu1,2, ZHAO Zhihong2
1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, China;
2. Key Laboratory of Traffic Safety and Control of Hebei Province, Shijiazhuang 050043, China
Abstract: To solve the difficulty of weak signal detection and aiming at the two features of chaotic oscillator that it is sensitive to weak signal and has immunity to noise, a new method of detecting weak signal based on the coupled Van der Pol-Duffing oscillator system is proposed. The dynamic behaviors of the coupled system under different parameters are compared, bifurcation diagrams and dichotomies are used to determine accurate critical threshold value, the weak signal detection principle based on phase diagram is expounded and a weak signal is successfully detected through the transition from chaotic to the periodic state and the signal-noise ratio threshold reaches -30 dB. The influence of noise on the system status under different accuracy amplitudes, influence of different frequency signals, and influence of the phase shift, are studied. Simulation results show that the coupled system is sensitive to weak signals under strong noise conditions and it is feasible to use it for weak signals detection.
Keywords: coupled system;Van der Pol-Duffing oscillator;chaos;weak signal detection
2018, 44(8): 107-112,119 收稿日期: 2017-11-10;收到修改稿日期: 2018-01-15
基金项目: 国家自然科学基金项目（11172182, 11227201, 11472179）
作者简介: 石兆羽(1989-),男,河北石家庄市人,硕士研究生,专业方向为非线性理论与故障诊断
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